HSC +2 Maths - Sample 5 Mark Questions - Part3

For Plus2 Maths Part1 and Part2 Important questions , watch these pages.

1) Examine the consistency of the system of equations:

       2x + 3y + 7z = 5,

       3x + y – 3z = 13,

       2x + 19y – 47z = 32.

2) Find the adjoint of the matrix and verify the result A(adj A) = (adj A) A = |A|.I

3)       (1) For any vector prove that

          (2) Find the projection of the vector on .

4) Find the vector and Cartesian equation of the sphere on the join of the points A and B having position vectors and respectively as a diameter. Find also the centre and radius of the sphere.

5) If P represents the variable complex number z, find the locus of P, if |2z-1| = |z-2|.

6) The headlight of a motor vehicle is a parabola reflector of diameter 12 cm and depth 4 cm. Find the position of bulb on the axis of the reflector for effective functioning of the head.

7) Obtain the Maclaurin’s series for .

8) Verify Lagrange’s law of mean for the function on [1, 3].

9) Given , where x=cos t; y=sin t; Find

10) Evaluate:

11) Solve:

12) G is a group, . Prove that

13) Construct the truth table for .

14) The overall percentage of passes in a certain examination is 80. If 6 candidates appear in the examination, what is the probability that at least 5 pass in examination?

15)      (1) State and prove cancellation laws on groups.
                                       (or)
           (2) Four coins are tossed simultaneously. What is the probability of getting (i) exactly 2 heads; (ii) at least 2 heads; (iii) almost 2 heads?

16) Find the shortest distance between the parallel lines and .

17) If n is a positive integer prove that

18) Find the equation to the two tangents that can be drawn from the point (1, 2) to the hyperbola .

19) Forces 2i+7j, 2i-5j+6k, -i+2j-k act at a point P whose position vector is 4i-3j-2k. Find the moment of the resultant of three forces acting at P about the point Q whose position vector is 6i+j-3k.

20) Prove that